To solve a puzzle, one needs to determine which cells will be boxes and which will be empty. Solvers often use a dot or a cross to mark cells they are certain are spaces. Cells that can be determined by logic should be filled. If guessing is used, a single error can spread over the entire field and completely ruin the solution. An error sometimes comes to the surface only after a while, when it is very difficult to correct the puzzle. The hidden picture plays little or no part in the solving process, as it may mislead. The picture may help find and eliminate an error.
Many puzzles can be solved by reasoning on a single row or column at a time only, then trying another row or column, and repeating until the puzzle is complete. More difficult puzzles may also require several types of "what if?" reasoning that include more than one row (or column). This works on searching for contradictions, e.g., when a cell cannot be a box because some other cell would produce an error, it must be a space.
At the beginning of the solution, a simple method can be used to determine as many boxes as possible. This method uses conjunctions of possible places for each block of boxes. For example, in a row of ten cells with only one clue of 8, the bound block consisting of 8 boxes could spread from:
As a result, the block must spread through the six centermost cells in the row.
The same applies when there are more clues in the row. For example, in a row of ten cells with clues of 4 and 3, the bound blocks of boxes could be:
This method consists of determining spaces by searching for cells that are out of range of any possible blocks of boxes. For example, considering a row of ten cells with boxes in the fourth and ninth cell and with clues of 3 and 1, the block bound to the clue 3 will spread through the fourth cell and clue 1 will be at the ninth cell.
First, the clue 1 is complete and there will be a space at each side of the bound block.
Second, the clue 3 can only spread somewhere between the second cell and the sixth cell, because it always has to include the fourth cell; however, this may leave cells that may not be boxes in any case, i.e. the first and the seventh.
In this method, the significance of the spaces will be shown. A space placed somewhere in the middle of an uncompleted row may force a large block to one side or the other. Also, a gap that is too small for any possible block may be filled with spaces.
For example, considering a row of ten cells with spaces in the fifth and seventh cells and with clues of 3 and 2: